Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions

The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an im...

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Autores principales:	Wisunee Puggard, Sa-Aat Niwitpong, Suparat Niwitpong
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	confidence interval Birnbaum–Saunders distribution coefficient of variation bootstrap generalized confidence interval Bayesian Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e4731014e9994b12b392d3a117d3a0d9
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id	oai:doaj.org-article:e4731014e9994b12b392d3a117d3a0d9
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spelling	oai:doaj.org-article:e4731014e9994b12b392d3a117d3a0d92021-11-25T19:06:58ZBayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions10.3390/sym131121302073-8994https://doaj.org/article/e4731014e9994b12b392d3a117d3a0d92021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2130https://doaj.org/toc/2073-8994The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.Wisunee PuggardSa-Aat NiwitpongSuparat NiwitpongMDPI AGarticleconfidence intervalBirnbaum–Saunders distributioncoefficient of variationbootstrapgeneralized confidence intervalBayesianMathematicsQA1-939ENSymmetry, Vol 13, Iss 2130, p 2130 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	confidence interval Birnbaum–Saunders distribution coefficient of variation bootstrap generalized confidence interval Bayesian Mathematics QA1-939
spellingShingle	confidence interval Birnbaum–Saunders distribution coefficient of variation bootstrap generalized confidence interval Bayesian Mathematics QA1-939 Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
description	The Birnbaum–Saunders (BS) distribution, which is asymmetric with non-negative support, can be transformed to a normal distribution, which is symmetric. Therefore, the BS distribution is useful for describing data comprising values greater than zero. The coefficient of variation (CV), which is an important descriptive statistic for explaining variation within a dataset, has not previously been used for statistical inference on a BS distribution. The aim of this study is to present four methods for constructing confidence intervals for the CV, and the difference between the CVs of BS distributions. The proposed methods are based on the generalized confidence interval (GCI), a bootstrapped confidence interval (BCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval. A Monte Carlo simulation study was conducted to evaluate their performances in terms of coverage probability and average length. The results indicate that the HPD interval was the best-performing method overall. PM 2.5 concentration data for Chiang Mai, Thailand, collected in March and April 2019, were used to illustrate the efficacies of the proposed methods, the results of which were in good agreement with the simulation study findings.
format	article
author	Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong
author_facet	Wisunee Puggard Sa-Aat Niwitpong Suparat Niwitpong
author_sort	Wisunee Puggard
title	Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
title_short	Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
title_full	Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
title_fullStr	Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
title_full_unstemmed	Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions
title_sort	bayesian estimation for the coefficients of variation of birnbaum–saunders distributions
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/e4731014e9994b12b392d3a117d3a0d9
work_keys_str_mv	AT wisuneepuggard bayesianestimationforthecoefficientsofvariationofbirnbaumsaundersdistributions AT saaatniwitpong bayesianestimationforthecoefficientsofvariationofbirnbaumsaundersdistributions AT suparatniwitpong bayesianestimationforthecoefficientsofvariationofbirnbaumsaundersdistributions
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Bayesian Estimation for the Coefficients of Variation of Birnbaum–Saunders Distributions

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